The formula for the volume ( V ) of a right rectangular prism is given on the FCAT formula sheet.

1. Today we will explore the Essential Question, “What is the process for using volume of a right rectangular prism to solve problems?" The focus of this lesson is on solving problems involving volume of a right rectangular prism. A right rectangular prism is a box-shaped figure that looks like the figure shown. The edges are called the length, width, and height and are denoted l, w, and h. h w l When building or covering a box, it is necessary to find the surface area. When filling the box, it is necessary to find the volume of the box. The formula for the volume (V) of a right rectangular prism is given on the FCAT formula sheet.

2. A B h h 8 cm 8 cm 12 cm 9 cm Example 1: Two rectangular boxes have the same height and the same length, but different widths, as shown in the figure. The difference in the volumes of Box B and Box A is 360 cubic centimeters. What is h, the height of each box in centimeters? Box A: Box B: Therefore, the height of each box is 15 centimeters.

3. x + 3 x 2x Example 2: A company needs to build a box whose dimensions can change but are always related as shown in the figure. Find a simplified formula, in terms of x, for the volume of the box.

4. 1.A shopping carton for computer parts is in the shape of a cube that measures 10 inches on each edge. In each of its bottom corners, the carton has one foam cube. Each foam cube measures 2 inches on an edge, as shown in the diagram. What is the volume, in cubic inches, of the empty space in the shipping carton when the 4 foam cubes are in the box? Guided Practice Problems: Shopping Carton: Small foam cube: 4 Small foam cubes: V = 4(8) = 32 Volume of empty space: 1000 – 32 = 968

5. h inches h inches A B 2 inches 2 inches 3 inches 5 inches Box B: Box A: 2.Two rectangular boxes have the same height and the same length, but different widths, as shown in the figure. The difference in the volumes of Box B and Box A is 36 cubic inches. What is h, the height of each box in inches? The height of each box is 9 inches.

6. 3 ft 8 ft 3 3 ft 8 9 3 8 19 19 ft 3.The diagram shows the dimensions of the cargo space in a moving van. What is the maximum volume of cargo, in cubic feet, that can fit in the van? The van is made up of a large prism adjoined to a small prism. 6 ft Small prism: Large prism: The volume of the cargo space in the van is the sum of the volumes of the two prisms. Therefore the total volume is 72 + 1368 or 1440 cubic feet.

7. height = x +2 length = x width = 3x 4. Find a simplified formula for the volume of the box shown in the diagram below. Show your work.

8. 40” 20” 10” 10” length = 5 height = 2x + 3 width = x Independent Practice: Complete the two sample questions finding the volume of a rectangular prism. Remember that tomorrow we will have our mini-assessment on this topic. You should prepare for this assessment by reviewing the examples, the guided practice problems and these problems. 1.Find a simplified formula for the volume of the box shown in the diagram. Show your work. 2. As shown in the diagram, a box with a square base is increased in size. The base remains the same but the height is increased from 20 inches to 40 inches. How many additional cubic inches are contained in the volume of the larger box? 4000 – 2000 = 2000 additional cubic inches in the larger box.